Rivergal,
What position do you put the rod in as you are netting the fish? If you are left handed, it should go back slightly over the left shoulder. You should bend or squat slightly down and come up with the right hand "net"under the fish. Under the best conditions, your body will slightly rotate to the left side as you do this.
Hugh

Thanks, Hugh. After setting the hook with my left arm,
I have been putting the rod in my right hand in order to net with my left.
I have had way more casting practice than netting practice, and it is hard to teach an old dog new tricks.

Rivergal
If you feel more comfortable doing it with the other hand. that's fine. Just reverse the side that I said and do the things mentioned. If you do want to learn to net right handed, you can practice those techniques in the yard and try putting them into practice when you;re on the water. It will feel a little more comfortable each time that you do it. It sounds like you need to build up the muscles on that side by just practicing with a little weight in the net.
Hugh

Hugh has you on track. When I net, I try not to chase the trout with the net. I get the net underwater and then lead the trout over the net like Hugh suggested with that turning motion of the body. When the trout is over the net. I simultaneously bring the net up and slightly lower the rod tip. I try to pay attention to where the line/ leader connection is in relation to the rod tip. A quick burst from the trout and that connection can cause just enough drag in the tip top to cost a good fish. Don't know if I would practice netting out in the yard. The neighbors might think you've gone nuts. Maybe indoors.

I'm left handed and cast left handed. I net with my right hand. On those rare occasions where I need a net, I do as Hugh said and just use the net in my right hand.

If you are left handed, you have a significant advantage over right handed people and here is what it is. The world is set up for a right handed person. For that reason, a left handed person has to use his/her right hand far more than right handed people have to use their left hand.

You probably already have far more manual dexterity and hand/eye coordination with your right hand than most right handed people have with their left hands.